# Tagged Questions

The study of discrete mathematical structures. Consider using a more specific tag instead, such as: (combinatorics), (graph-theory), (computer-science), (probability), (elementary-set-theory), (induction), (recurrence-relations), etc.

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### Prove for any number n, it is possible to select $X = 2^n$ numbers from $2^{n+1}$ numbers s.t. the sum of X is divisible by $2^n$

Prove, for any natural number $n$, that it is possible to select $2^n$ numbers from any collection of $2^{n+1}$ natural numbers such that that sum of the $2^n$ numbers is divisible by $2^n$. I am not ...
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I'm having trouble figuring out how we are arriving at this particular solution Use equivalences to transform the following wff into a CNF. (Conjuctive Normal Form). $(P \rightarrow (Q \rightarrow P)... 1answer 38 views ### Eulerian graph from vertex subsets Let$K_{n1,n2,...,n\ell}$, where$\ell \geq 3$, denote a graph for which the vertex set is partitioned into$\ell$subsets of respective size$n_1, n_2, ..., n_\ell$and any two vertices are adjacent ... 1answer 27 views ### How do I correctly show a proof of this implication and refute it's converse? If there is a valid implication between the two, show the proof. If not, refute it by giving a counter example. 1)$x+5>8$2)$\left| x \right| >3$$$x+5>8\Rightarrow \left| x \right| >... 1answer 150 views ### Eulerian graph with odd/even vertices/edges Find an Eulerian graph with an even/odd number of vertices and an even/odd number of edges or prove that there is no such graph (for each of the four cases). I came up with the graphs shown below ... 1answer 14 views ### Looking to find a lower bound to this term I have this term I'm trying to bound(below). From numerical experimentation I'm fairly confident that the bound is 1/2. I've been out of school for a couple years and my proof skills have diminished ... 2answers 25 views ### How do I point out whether the propositions are implying one another? 1) It’s raining but the birds chirp. 2) If it’s not raining then the birds chirp. 3) It’s raining or the birds do not chirp. For each pair of propositions, point out whether the second is implied ... 1answer 103 views ### Line graph and Eulerian graph Let G be a simple, undirected and connected graph for which every vertex has degree r. Prove that the line graph G' of G is Eulerian. So, basically we have two options for r, either it is ... 1answer 54 views ### Control theory - what method is used to find the discrete time control system here We are given a car model:$$\dot x = V\cos(a) \quad \dot y = V\sin(a) \quad \dot a = u$$V some arbitrary number Make an (first order) approximation$$\dot x = V \quad \dot y = Va \quad \dot a = ... 3answers 32 views ### How do I figure out if these two statements imply one another? $$x^2>9\Rightarrow |x|>3 \quad \quad |x|>3\Rightarrow x^{ 2 }>9$$ If there is a valid implication between the two, I must show the proof. If not, I must refute it by giving a counter ... 2answers 29 views ### Set theory : Anti-symmetric but transitive (proof) The exam practice question is as follows: We call a relation$R$anti-reflexive iff$\forall a \in A : (a,a) \notin R$and anti-symmetric iff$\forall a,b \in A : (a,b) \in R \rightarrow (b,...
Recently, I read the statement "Fix $k\geq 1$, Any tree with at least $k$ edges may be decomposed as a union of edge-disjoint subtrees, each having between $k$ and $3k$ edges" Now I was wondering ...